RISK, COST OF CAPITAL, AND CAPITAL BUDGETING This topic applies the concept of NPV to risky cash flows. NPV = C o + Σ C t ¯ /(1+r) t r = discount rate use to the determine the NPV of risky project can be computed from CAPM(or APT).

THE COST OF EQUITY CAPITAL The discount rate of a project should be the expected return on a financial asset of comparable risk. The discount rate of a project should be the expected return on a financial asset of comparable risk. From the firm’s perspective, the expected return is the cost of equity capital. CAPM From the firm’s perspective, the expected return is the cost of equity capital. CAPM Ř = R f + β(Ř m – R f )

continue Example: The stock of the Q, has beta of 1.3. The firm is 100% equity financed. The risk free rate is 7%. What is the appropriate discount rate for these new project, assuming a market risk premium of 9.5%? Example: The stock of the Q, has beta of 1.3. The firm is 100% equity financed. The risk free rate is 7%. What is the appropriate discount rate for these new project, assuming a market risk premium of 9.5%? Example: expected return = 5%+(1.21x9.5%) = %. Assuming Co = 100 Example: expected return = 5%+(1.21x9.5%) = %. Assuming Co = 100 ProjβC1IRRNPVAccept or Reject A %20.2Accept B Accept C Reject

ESTIMATION OF BETA Beta of security i = Cov(R i,R m )/Var(R m ) = σ i,M /σ 2 M Example: return on the stock G and S&P500 YearR G R M (S&P500) 1-10%-40%

continue Problems 1.Betas may vary over time 2.The sample size may be inadequate 3.Betas are influenced by changing financial leverage and business risk Solutions 1.Problems 1 & 2 can be moderated by more sophisticated statistical techniques 2.Problem 3 can be lessened by adjusting for changes in business and financial risk 3.Look at average beta estimates of several comparable firms in the industry Solutions

DETERMINANTS OF BETA 1. Cyclicality of Revenues. The revenues of some firms are quite cyclical. Highly cyclical stocks have high betas. 2. Operating leverage  refers to the firm’s fix costs of production. [(change in EBIT/EBIT)X(sales x change in sales)] 3. Financial Leverage and Beta. β Asset = [{Debt x β Debt /(Debt+Equity)}+{Equity x β Equity /(Debt+Equity)}] Assumpt, The beta of debt is zero, β Asset =[{Equity x β Equity /(Debt+Equity}] or β Equity = [{ β Asset {1 + (Debt/Equity)}]

Example Consider a tree-growing company, is currently all equity and has a beta of 0.8. The firm has decided to move to a capital structure of one part debt to two parts equity. Because the firm is staying in the same industry, its asset beta should remain at 0.8. However, assuming a zero beta for its debt, its equity beta would become β Equity = [{ β Asset {1 + (Debt/Equity)}] 1.2 = 0.8{1 + (1/2)} 1.2 = 0.8{1 + (1/2)} If the firm had one part debts equity in its capital structure, its equity beta would be 1.6 = 0.8(1 + 1) The effect of leverage, then, is to increase the equity beta

The cost of capital with debt If a firm uses both debt and equity, the cost of capital is a weighted average of each. If a firm uses both debt and equity, the cost of capital is a weighted average of each. [{S x r S /(S + B)} + {B x r B /(S + B)}] The average cost of capital (after tax) for the firm (r WACC ): The average cost of capital (after tax) for the firm (r WACC ): = [{S x r S /(S + B)} + {B x r B x (1 – T C )/(S + B)}] Example: Consider a firm whose debt has a market value of $40 million and whose stock has market value of $60 million (3 million outstanding shares of stock, each selling for $20 per share). The firm pays a 15 percent rate of interest on its new debt and has a beta of The corporate tax rate is 34 percent. (Assuming that the SML holds, that the risk premium on the market is 9.5 percent, and that the current Treasury bill rate is 11 percent). What is this firm’s r WACC ?

continue Three values are computed below Three values are computed below 1. The pretax cost of debt is 15 percent, implying an after tax cost of 9.9 percent.[15%x(1 – 0.34)]. 2. The cost of equity capital is computed by using the SML. r S = 24.40%. 3. r WACC = [{S x r S /(S + B)} + {B x r B x (1 – T C )/(S + B)}] = {(60/100)x24.40%} + {(40/100)x9.9%}= 18.60%

Example Suppose that a firm has a both a current and a target debt-equity ratio of 0.6, a cost of debt of percent, and a cost a equity of 20 percent. The corporate tax rate is 34 percent. r WACC = [{S x r S /(S + B)} + {B x r B x (1 – T C )/(S + B)}] = {6x20%/(6+10)}+{(10x0.66x0.66/(6+10)} = 16.25% Suppose the firm is considering taking on a warehouse renovation costing $50 million that is expected to yield cost saving of $12 million a year for six year. Using the NPV eq and discounting the six years of expected cash flows from the renovation at the r WACC, NPV = -$50 + {$12/(1+ r WACC )} + … + {$12/(1+ r WACC ) 6 } = -$50 + $12 x A = -$50 + $12 x A = -$50 + (12 x 3.66) = -$6.07 (reject the project) = -$50 + (12 x 3.66) = -$6.07 (reject the project)